The Grinch from the cartoon/book is an AU Kris Kringle/Claus.Let's say that the animals couldn't get to Claus in time to protect him from the Winter Warlock. The Warlock discovers him, and as evil as he is, he cannot bring himself to kill a child. He raises him as his own - instilling him with a hatred of all things good and fun. Somewhere in the Grinch's young adult years, he comes across a lost dog from Sombertown and takes him in, thus explaining how he got Max. Eventually, the Warlock passes on as a mean and despicable creature due to Claus never showing up to help him, and leaves the mountain to "Grinch", as he has come to be called. Perhaps due to a split in time, somebody else has taken on the role of Santa Claus and has gone along a similar path that The Grinch would have (i.e. becoming a world-renowned giftgiver). Sombertown, once the Burgermeister falls out of power, becomes a happier place and is renamed Whoville to reflect this.
The film and Horton Hears a Who! are in the same universe.The film is set on a snowflake, but as noted in the main page, it could be the speck of dust on the snowflake. Once the snowflake melts, the speck attached itself to a flower in the Jungle of Nool and stayed there. As for the Who's, let me explain my hypothesis: The Grinch is actually the same species as the Who's. He is a different subspecies though, explaining his greenness. The 'Grinch' kind of Who are actually quite numerous, but live quite a distance away from Whoville. Sometime after the events of the film, the 'Grinch' kind of Who's, for some reason or another, relocate to Whoville. The Who's seen in Horton Hears A Who are the result of generations of interbreeding between the two kind of Who's, which also explains the remarkably different Whoville in the film and all the weird technology.
Dr. Seuss originally intended the Grinch to be just another WhoIn the original illustrations, the Grinch's eyes are the only aspect that makes him look different from the Whos. When Chuck Jones painted him green, people assumed he was some kind of cave monster, leading to his "mutant" backstory in the live-action version. Dr. Seuss envisioned him as a hermit who lived in a cave and "Grinch" as a nickname instead of a species name.
The Whos are humanoid insects.Cindy Lou Who (who is no more than 2) is clearly a larva. She has no visible legs, and she, and all the other younger Whos, have visible antennae that the adult Whos don't have. At some point in her development, she will enter a pupal stage, and emerge with legs and less obvious antennae.